The generator matrix

 1  0  1  1  1 3X+2  1  1 3X  1  1 X+2 3X+2  2  1  1  2  1  1  1  1  0  1  1  1 3X  1  1  1 2X+2  0  1  1  1  1  1  1  1 3X  1  1 2X 2X  1 X+2 X+2  0  1 3X  1 2X+2  1  1  X
 0  1  1  2 X+1  1  X 2X+1  1 3X X+3  1  1  1  2 2X+3  1 X+1  X 3X+2 2X+3  1 X+3 2X 3X+2  1 2X+2 2X  X  1  1  3 3X+3 2X X+2 X+1 2X+1 3X+3  1  2 3X+2  1  1 X+2  1  1 2X+2 2X+1  1  0  1 X+2  0  0
 0  0  X 3X 2X 3X 3X 2X 3X+2  0  X  0 2X+2  2 3X+2 2X+2  X 3X+2 2X+2 3X X+2 X+2  2  X 2X  2  0 2X+2 X+2 X+2 3X  0 X+2 X+2  2  X 2X+2 2X  0 2X+2 X+2  2 2X 3X+2 X+2 3X+2  X 3X+2 3X 3X+2  2 2X X+2 X+2

generates a code of length 54 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+306x^51+272x^52+456x^53+176x^54+300x^55+228x^56+204x^57+24x^58+54x^59+12x^61+12x^63+1x^64+1x^68+1x^76

The gray image is a code over GF(2) with n=432, k=11 and d=204.
This code was found by Heurico 1.16 in 0.125 seconds.